OxfordAQA International AS and A-level Physics: SI units and conversions, error treatment and order-of-magnitude estimation (9630) – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions follow section 3.1 (3.1.1 to 3.1.3) of the OxfordAQA International AS and A-level Physics (9630) specification, Version 4.4, which is shared content for the International AS and the International A-level. Teaching is in the study guide and revision notes. Course pages: hub and checklist. Where a question needs the elementary charge, it is given as e = 1.60 × 10⁻¹⁹ C.

Questions

1. Convert (i) 2.8 cm² to m², (ii) 13.6 g cm⁻³ to kg m⁻³, (iii) 90 km h⁻¹ to m s⁻¹. [3]

2. (a) A particle has kinetic energy 1.4 MeV. Express this in joules. [2] (b) An electron in an atom changes energy by 6.4 × 10⁻¹⁹ J. Express this in eV. [1]

3. An electric shower of power 3.0 kW is used for 12 minutes each day. (a) Calculate the energy transferred per day in kW h. [2] (b) Express this in joules. [1] (c) Calculate the energy transferred in 30 days, in MJ. [1]

4. A digital balance shows +0.4 g with nothing on the pan. A coin is then placed on it five times and the readings are 7.52, 7.49, 7.51, 7.50 and 7.53 g. (a) State the type of error shown by the reading with nothing on the pan. [1] (b) Calculate the corrected mean mass. [1] (c) Explain why taking more readings does not remove this error. [1] (d) Estimate the uncertainty in the mean from the spread of the readings. [1]

5. Match each statement to one of these terms: accuracy, precision, repeatability, reproducibility, resolution. (a) A digital timer displays to 0.01 s. [1] (b) Five timings of a period lie between 1.51 s and 1.53 s. [1] (c) The same student repeats the experiment on another day with the same kit and gets the same mean. [1] (d) A different group using different timers and a different method obtains a mean that agrees. [1] (e) The mean differs from the accepted value by only 0.3%. [1]

6. A length is measured as 0.842 m ± 0.003 m. (a) Calculate the fractional uncertainty. [1] (b) Calculate the percentage uncertainty. [1] (c) A second length, 0.640 m, has a percentage uncertainty of 2.5%. Calculate its absolute uncertainty. [1] (d) Write the second length with its uncertainty, using a suitable number of significant figures. [1]

7. The power dissipated in a resistor is P = V²/R. V = 12.0 ± 0.2 V and R = 47 ± 2 Ω. Calculate P and its absolute uncertainty, and state the result with its uncertainty. [5]

8. The temperature θ of a heated liquid is plotted against time t, with each θ having an uncertainty of ±2 °C. The best-fit line passes through (0, 21) and (10, 60). The steepest line through all the error bars passes through (0, 19) and (10, 62); the shallowest passes through (0, 23) and (10, 58). Temperatures are in °C and times in minutes. (a) Calculate the gradient of the best-fit line. [1] (b) Calculate the gradients of the steepest and shallowest lines. [2] (c) State the uncertainty in the gradient. [1] (d) State the intercept on the θ axis, with its uncertainty. [2] (e) Calculate the percentage uncertainty in the gradient. [1]

9. (a) Three students quote a result as A: 4.56 ± 0.1, B: 4.6 ± 0.1, C: 4.6 ± 0.12. State which is consistent, and give a reason why each of the others is not. [3] (b) A calculation gives 0.0472 with an uncertainty of 0.0036. Write the result in a suitable form. [2]

10. Estimate the number of times a car wheel turns during a 10 km journey. State your assumption and give the answer to the nearest order of magnitude. [4]

11. A raindrop of radius 2 mm falls at 7 m s⁻¹. The density of water is 1000 kg m⁻³. (a) Calculate the mass of the drop. [2] (b) Calculate its kinetic energy and state the order of magnitude in J. [2] (c) Express the energy in eV and state the order of magnitude. [2]

Answers

1. (i) 1 cm² = 10⁻⁴ m², so 2.8 × 10⁻⁴ m² [1]. (ii) 13.6 × 10⁻³ kg ÷ 10⁻⁶ m³ = 1.36 × 10⁴ kg m⁻³ [1]. (iii) 90 × 1000 ÷ 3600 = 25 m s⁻¹ [1]. [3] Examiner insight: Show the conversion factor you used for the squared and cubed units, because a bare answer with the wrong power of ten shows nothing of your method.

2. (a) 1.4 MeV = 1.4 × 10⁶ eV [1]; × 1.60 × 10⁻¹⁹ = 2.2 × 10⁻¹³ J (2.24 × 10⁻¹³) [1]. (b) 6.4 × 10⁻¹⁹ ÷ 1.60 × 10⁻¹⁹ = 4.0 eV [1]. [3] Examiner insight: Write the prefix as a power of ten before multiplying; skipping that step is a frequent route to an answer a million times too small.

3. (a) 12 min = 0.20 h [1]; energy = 3.0 × 0.20 = 0.60 kW h [1]. (b) 0.60 × 3.6 × 10⁶ = 2.2 × 10⁶ J (2.16 × 10⁶) [1]. (c) 30 × 2.16 × 10⁶ = 6.48 × 10⁷ J = 65 MJ [1]. [4] Examiner insight: Convert minutes to hours before using kW h; using 12 directly is a common error that spoils every later part.

4. (a) Systematic (zero) error [1]. (b) Mean = 7.51 g; corrected = 7.51 − 0.4 = 7.11 g [1]. (c) The offset is the same size and direction in every reading, so averaging leaves it unchanged [1]. (d) Half-range = (7.53 − 7.49) ÷ 2 = ±0.02 g [1]. [4] Examiner insight: Say that the error is the same size every time; stating only that repeats are “not helpful” does not explain why.

5. (a) Resolution [1]. (b) Precision [1]. (c) Repeatability [1]. (d) Reproducibility [1]. (e) Accuracy [1]. [5] Examiner insight: Precision and accuracy are different words: a tight spread about the wrong value is precise but not accurate, so say which one the data support.

6. (a) 0.003 ÷ 0.842 = 0.0036 [1]. (b) 0.36% [1]. (c) 0.025 × 0.640 = 0.016 m [1]. (d) One significant figure for the uncertainty: 0.64 ± 0.02 m [1]. [4] Examiner insight: Match the decimal places of the value to those of the uncertainty; 0.640 ± 0.02 m is inconsistent.

7. P = 12.0² ÷ 47 = 3.06 W [1]. Percentage uncertainty in V = 0.2 ÷ 12.0 = 1.67% [1]. Percentage uncertainty in R = 2 ÷ 47 = 4.26% [1]. V is squared: total = 2 × 1.67 + 4.26 = 7.6% [1]. Absolute uncertainty = 0.076 × 3.06 = 0.23 W, so P = 3.1 ± 0.2 W [1]. [5] Examiner insight: Show the doubling for the squared term explicitly; the final figure alone is hard to credit if it contains an arithmetic slip.

8. (a) (60 − 21) ÷ 10 = 3.9 °C per minute [1]. (b) Steepest: (62 − 19) ÷ 10 = 4.3 [1]. Shallowest: (58 − 23) ÷ 10 = 3.5 [1]. (c) (4.3 − 3.5) ÷ 2 = ±0.4 °C per minute [1]. (d) Best intercept 21 °C; the extreme intercepts are 19 and 23, so uncertainty = (23 − 19) ÷ 2 = ±2 °C [1] [1]. (e) 0.4 ÷ 3.9 × 100 = 10% [1]. [7] Examiner insight: Use points far apart when finding a gradient and give units; the half-difference of the extreme lines is worth stating in words as well as giving the number.

9. (a) B is consistent [1]. A gives the value to more decimal places than its uncertainty supports [1]. C gives the uncertainty to more decimal places than the value [1]. (b) Uncertainty to 1 significant figure: 0.004 [1]; value to the same decimal place: 0.047 ± 0.004 [1]. [5] Examiner insight: Give a reason that mentions decimal places or significant figures; “looks wrong” does not identify the problem.

10. Assume wheel diameter about 0.6 m [1]. Circumference = π × 0.6 = 1.9 m [1]. Turns = 10 000 ÷ 1.9 = 5.3 × 10³ [1]. Since 5.3 is above about 3.2, the order of magnitude is 10⁴ [1]. [4] Examiner insight: Always state the assumption you used; an unstated size cannot be checked against a sensible range.

11. (a) Volume = 4/3 × π × (2 × 10⁻³)³ = 3.4 × 10⁻⁸ m³ [1]; mass = 1000 × 3.35 × 10⁻⁸ = 3.4 × 10⁻⁵ kg [1]. (b) KE = ½ × 3.35 × 10⁻⁵ × 7² = 8.2 × 10⁻⁴ J [1]; order of magnitude 10⁻³ J [1]. (c) 8.2 × 10⁻⁴ ÷ 1.60 × 10⁻¹⁹ = 5.1 × 10¹⁵ eV [1]; order of magnitude 10¹⁶ eV [1]. [6] Examiner insight: Convert the radius from mm to m before cubing; the cube makes any error in that step very large.

Where marks are usually lost

• Converting mm², cm³ and similar units with the linear factor.
• Leaving a prefix in an equation, such as using 250 for 250 mA.
• Using minutes in a kW h calculation without converting to hours.
• Describing a systematic error as something repeating can fix.
• Using accuracy and precision as if they meant the same.
• Not doubling the percentage uncertainty for a squared quantity.
• Quoting a result with more decimal places than its uncertainty.
• Subtracting uncertainties, or adding absolute uncertainties in a product.
• Drawing extreme lines that miss error bars, or finding gradients from points close together.
• Giving an order of magnitude with no stated assumptions or rounding the wrong way at the boundary.

Next steps

• Review with the revision notes and the study guide.
• Go to the OxfordAQA A-level Physics hub or the printable checklist.
• Take one of the free 10-minute diagnostics.
• Book a free trial class.

Official syllabus

OxfordAQA International AS and A-level Physics (9630), Version 4.4, section 3.1 Measurements and their errors, for International AS and A-level exams from May/June 2020 onwards. Published by OxfordAQA.